Question

As player salaries have increased, the cost of attending baseball games has increased dramatically. The data below represents the cost of four tickets, two beers, four soft drinks, four hot dogs, two game programs, two baseball caps, and the parking fee for one car for each of the 30 Major League Baseball teams in 2011:

174, 339, 259, 171, 207, 160, 130, 213, 338, 178, 184, 140, 159, 212, 121, 169, 306, 162, 161, 160, 221, 226, 160, 242, 241, 128, 223, 126, 208, 196

Decide whether the data appears to be approximately normally distributed by

(a) comparing data characteristics to theoretical properties.

(b) constructing a normal probability plot.

Answer 1

Solution-:

> x=c(174,339,259,171,207,160,130,213,338,178,184,140,159,212,121,169,306,162,161,160,221,226,160,242,241,128,223,126,208,196);x
[1] 174 339 259 171 207 160 130 213 338 178 184 140 159 212 121 169 306 162 161
[20] 160 221 226 160 242 241 128 223 126 208 196
> #(a)
> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
121.0 160.0 181.0 197.1 222.5 339.0
> mean(x)
[1] 197.1333
> #for mode
> tx=table(x);
> m=which(tx==max(tx))
> stx=sort(unique(x))
> Mode=stx[m];
> Mode
[1] 160
> # Here, Mean=197.33, Median=181 and Mode=160 are notequal so this data is not satisfy property of normal distribution.
> #(b)
> #For check normality
> shapiro.test(x)

Shapiro-Wilk normality test

data: x
W = 0.90476, p-value = 0.011

> #Conclusion:- If pvalue=0.011< l.o.s.= \alpha=0.05 then we reject the hypothesis of normality. We say that data is not normal.
> #Or
> qqnorm(x)
> qqline(x)

Normal Q-Q Plot o 0 o 300 o 250 Sample Quantiles 200 Donecos 000000 150 -2 -1 0 1 N Theoretical Quantiles

> #This graph shows non-normal probability plot.

R-Code:

x=c(174,339,259,171,207,160,130,213,338,178,184,140,159,212,121,169,306,162,161,160,221,226,160,242,241,128,223,126,208,196);x
#(a)
summary(x)
mean(x)
#for mode
tx=table(x);
m=which(tx==max(tx))
stx=sort(unique(x))
Mode=stx[m];
Mode
# Here, Mean=197.33, Median=181 and Mode=160 are notequal so this data is not satisfy property of normal distribution.
#(b)
#For check normality
shapiro.test(x)
#Conclusion:- If pvalue=0.011< l.o.s.= \alpha=0.05 then we reject the hypothesis of normality. We say that data is not normal.
#Or
qqnorm(x)
qqline(x)
#This graph shows non-normal probability plot.